Question

what is the difference between the sum of the first 20032003 even counting numbers and the sum of the first 20032003 odd counting numbers?

Answer 1

Answer: The difference between sum of first 20032003 even numbers and sum of first 20032003 odd numbers is “-20032003”.

Step-by-step explanation:

The sum of first 20032003 even numbers:

$Summation E=E_{1}+E_{2}+E_{3}+ . . . . . +E_{20032003}$

The sum of first 20032003 odd numbers:

$Summation O=O_{1}+O_{2}+O_{3}+ . . . . . +O_{20032003}$

Difference between the sum of first 20032003 even numbers and the sum of first 20032003 odd numbers:

$Difference=Summation E - Summation O=(E_{1}+E_{2}+E_{3}+ . . . . . . . +E_{20032003})-(O_{1}+O_{2}+O_{3}+ . . . . . . . +O_{20032003})$

$Difference=(E_{1}-O_{1})+(E_{2}-O_{2})+(E_{3}-O_{3})+ . . . . . . . +(E_{20032003}-O_{20032003})$

Even numbers start as 0, 2, 4, 6…. While odd numbers start as 1, 3, 5, 7…..

(assuming that we are taking non-negative even/odd numbers into account only)

As we know, every nth even number is one behind their respective odd number (i.e. 0 lags 1, 2 lags 3, 4 lags 5 and so on)

Thus, our equation of difference becomes,

$Difference=(-1)_{1}+(-1)_{2}+(-1)_{3}+ . . . . . . . +(-1)_{20032003} =(-1)*20032003=-20032003$

Learn more about even & odd numbers here brainly.com/question/24657250

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